The slope of the given equation is 0.075 and y-intercept is 0.125
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The point with coordinate having same slope as with given coordinates can be plotted on the same line.
First writing the given equation in standard slope intercept form :
y = mx + c.........(1)
In which:
• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
• c is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function
8y = 0.2(3x - 5)
8y = 0.6x - 1
y = 0.6/8x - 1/8
y = 0.075x - 0.125
Now, comparing it with equation (1) we get :
m = 0.075 and c = - 0.125
hence the slope of the given equation is 0.075 and y-intercept is 0.125
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Tell whether the graph would be continuous or discrete2. A pet store is selling puppies for $200 each. It has 8 puppies for sale.AcontinuousB) discrete
Given:
Cost of each puppy = $200
Number of puppies = 8
Here, the equation for total cost of puppies will be:
C = 200x
Where x represents the number of puppies sold
Cost of 1 puppy = $200
Cost of 2 puppies = $200(2) = $400
Cost of 3 puppies = $200(3) = $600
If you continue with the pattern you'll see the graph has a rate of change of 200
To determine if the graph will be continuous or discrete, we have:
For a graph to be continuous, the points on the graph must be connected with a continuos line, while for a graph to be discrete the points are series of unconnected points just like in a scatter plot.
The graph of this will be a discrete graph. A discrete graph have set of values(points)
ANSWER:
B. discrete
which point lies on the wall with point slope equation y+5=2(x+8)
The slope intercept form of equation is given as
(y - y1) = m(x - x1)
Where m = slope
From the equation: y + 5 = 2(x + 8)
Equate y + 5 = 0 and x + 8 = 0
y + 5 = 0
y = 0- 5
y = -5
For x + 8 = 0
x + 8 = 0
x = 0 - 8
x = -8
Hence, the point is (-8, -5)
The answer is (-8, -5)
Twenty students choose a piece of fruit from a list of 4 fruits: apple, banana, grape, and pear. The theoretical probability that a student will choose a banana is .25. Only 1 student chooses a banana. How can the experimental probability get closer to the theoretical probability?A. only give two choices of fruitB. use a smaller sample size of studentsC. use a larger sample size of studentsD. provide more choices of fruit
Total number of student 20.
Total number of fruits are 4.
The theoretical probability that a student will choose a banana is 0.25
The experimental probability is 1/20=0.05.
Thus there is a huge difference in the theoritical probability and experimental probability.
Thus the experimental probability get closer to the theoretical probability is:
A. only give two choices of fruit.
Help me please I've watched like five videos and still don't get it!
14)
Given data:
The given triangle.
As all the sides of the triangle are equal, it means all the angles are equal. The expression for the angle sum property of the triiangle is,
[tex]\begin{gathered} x+x+x=180^{\circ} \\ 3x=180^{\circ} \\ x=60^{\circ} \end{gathered}[/tex]In the given triangle each angle is 60 degree, so it is an acute angle triangle.
Thus, the given triangle is an acute angle triangle, so first option is correct.
15)
The all sides and all angles of the triangle are equal.
Thus, the given triange is an equilateral triangle, so third option is correct.
Bella competed in the 5,000 m race at the Olympics she finished in the race 14.2 minutes after the race Bella wrote the equation c equals 18.1 m to model the relationship between the number of calories she burned c and the number of minutes she ran m.how many calories did Bella burn in the first 10 minutes of the 5,000 meter race.
Answer
She burnt 181 calories in that first 10 minutes of the 5,000 meter race.
Explanation
Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as
c = 18.1m
The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.
That is, find c when m = 10 minutes
Recall,
c = 18.1m
c = 18.1 (10)
c = 181 calories.
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which graph show the solution set for -1.1×+6.4>-1.3
Problem
-1.1x + 6.4 > - 1.3
Concept
Solve for x by collecting like terms.
A graph has age (weeks) on the x-axis, and height (inches) on the y-axis. Points are grouped closely together. One point is outside of the cluster. Which statement is true? There is no relationship between the height of the plant and its age. Although the outlier is an extreme value, it should be included in the interpretation. By excluding the outlier, a better description can be given for the data set
Answer:
Step-by-step explanation:
The answer is C
Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends
Explanation:edge 2022
Solve this system of linear equations. Separatethe x- and y-values with a comma.7x - by = -414x + 5y = 43
Answer
x = 2, and y = 3
Explanation:
given the following linear equation
7x - 6y = -4------------- equation 1
14x + 5y = 43 ---------- equation 2
This equation can be solve simultaneously by using elimination method
Step 1 : eliminate x
To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1
7x * 2 - 6y * 2 = -4 * 2
14x * 1 + 5y * 1 = 43 * 1
14x - 12y = -8 ----------------- equation 3
14x + 5y = 43------------------ equation 4
Substract equation 4 from3
(14x - 14x) - 12 - 5y = -8 - 43
0 - 17y = -51
-17y = -51
Divide both sides by -17
-17y/-17 = -51/-17
y = 51/17
y = 3
To find x, put the value of y into equation 1
7x - 6y = -4
7x - 6(3) = -4
7x - 18 = -4
Collect the like terms
7x = -4 + 18
7x = 14
Divide both sides by 7
7x/7 = 14/7
x = 2
Therefore, x = 2 and y = 3
Melanie went shopping and spent $18 on scarves. If she spent $77 total, what percentage did she spend on scarves? Round your answer to the nearest percent.
Answer:
23.4%
Step-by-step explanation:
[tex]\frac{18}{77} =\frac{x}{100}[/tex]
$18 divided by $77 is the equivalent of X(% spent on scarves) divided by 100. To find X you cross multiply and divide. [tex](18*100)/77=23.377...[/tex], rounded, X = 23.4
I'm confused about this problem can someone explain?
Answer:
32.50x + 7.50 < 235
Step-by-step explanation:
All the cost have to be less than 325. x stands for the number of people buying tickets.
a bread recipe calls for 3 3/8 cups of white flour and 2 1/2 cups of whole wheat flour. How many cups of flour in all?
Answer:
5 complete cups and 7/8 of a cup
[tex]5\frac{7}{8}[/tex]A data set includes weights of garbage discarded in one week from 62 different households. The paired weights of paper and glass were used to obtain the results shown to the right. Is there sufficient evidence to support the claim that there is a linear correlation between weights of discarded paper and glass? Use a significance level of α=0.05. correlation matrix: Variables Paper Glass Paper 1 0.1983 Glass 0.1983
There is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
Given,
A data set includes weights of garbage discarded in one week from 62 different households.
significance level of α=0.05.
Now, According to the question:
The correlation matrix provided is:
Variables Paper Glass
Paper 1 0.1853
Glass 0.1853 1
The hypothesis for the test is:
H₀: ρ = 0 vs. H₀: ρ ≠ 0
The test statistic is:
r = 0.1983 ≈ 0.198
As the alternate hypothesis does not specifies the direction of the test, the test is two tailed.
The critical value for the two-tailed test is:
[tex]r_{alpha}/2, (n -2) = r_{0.005}/2 ,(62-2) = 0.250[/tex]
The conclusion is:
Because the absolute value of the test statistic is less than the positive critical value, there is not enough evidence to support the claim that there is a linear correlation between the weights of discarded paper and glass for a significance level of α = 0.05.
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16. Eric is deciding how many trees to plant.
Here are his estimates of the time it will take.
Number of trees
1 tree
2 trees
3 trees
4 trees
5 trees
Time
30 minutes
40 minutes
50 minutes
60 minutes
70 minutes
With each additional tree , the estimated time increases by 10 minutes .
in the question ,
a table with number of trees and time required to plant them is given .
For planting 1 tree 30 minutes is required to plant them .
for planting 2 trees 40 minutes is required to plant them .
increase in number of tree = 2 tree - 1 tree = 1 tree
change in time required = 40 min - 30 min = 10 min
for planting 3 trees , 50 minutes is required to plant them .
increase in number of tree = 3 trees - 2 trees = 1 tree
change in time required = 50 min - 40 min = 10 min
So, we can see that for every additional tree planted the time increases by 10 minutes .
Therefore , with each additional tree , the estimated time increases by 10 minutes .
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Figure 1 and Figure Il are similar figures. Figure I Figure II R S А B F C w T E D V U Which proportion must be true?
From the diagram,
CD is corresponding to WR
VW is corresponding to BC
RS is corresponding to DE
ST is corresponding to EF
TU is corresponding to FA
Final answer
[tex]\frac{ST}{EF}\text{ = }\frac{WR}{CD}[/tex]How many triangles can be formed by joining the vertices of a 10-sided polygon?
The total number of triangles formed by joining vertices of 10-sided polygon is given by the combination of 10 sides taken at 3, i.e. selection of 3 points from 10 points ( because a triangle has 3 vertices). This gives
[tex]10C3=\frac{10!}{3!(10-3)!}=\frac{10!}{3!\cdot7!}=\frac{10\cdot9\cdot8}{6}=\frac{720}{6}=120[/tex]Then, the answer is the last option: 120
The table shows the volume of water released by a dam over a certain period of time. Graph a line representing the data in the table, and find the slope and y-intercept of the line from the graph. Then enter the equation for the graph in slope-intercept form.
Okay, here we have this:
Considering the provided information. we are going to calculate the slope, and y-intercept of the line, so we obtain the following:
First we will calculate the slope using the following formula:
m=(y2-y1)/(x2-x1)
m=(80000-40000)/(10-5)
m=40000/5
m=8000
y-intercept:
y=mx+b
40000=(8000)5+b
40000=40000+b
b=0
Finally we obtain that the equation of the line is: y=8000x.
Let's graph the equation:
Liz is collecting aluminum cans for a school fundraiser. So far, she has collected 16 cans, which is 20% of her goal. How many cans must she collect to reach her goal?Parts A & B
Given the word problem, we can deduce the following information:
1. Liz collected 16 cans, which is 20% of her goal.
To determine the number of cans that Liz needs to collect to reach her goal, we use below equation:
[tex]0.20x=16[/tex]where:
x= total number of cans that Liz needs to collect
So,
[tex]\begin{gathered} 0.20x=16 \\ \text{Simplify} \\ x=\frac{16}{0.20} \\ x=80 \end{gathered}[/tex]Hence, the total number of cans is 80.
A.
To complete the double number line, we must determine first the other percent values. It the goal is 100%, we must subtract 20% from 100% and divide it by 4 to get the remaining percent values. So,
[tex]\frac{100-20}{4}=20[/tex]So the other percent values are:
0%
20%
20%+20%=40%
40%+20%=60%
60%+20%=80%
80%+20%=100%
To determine the amount of cans for each percent value,the process is shown below:
[tex]80(\frac{40}{100})=32[/tex][tex]\begin{gathered} 80(.6)=48 \\ \end{gathered}[/tex][tex]80(.8)=64[/tex][tex]80(\frac{100}{100})=80[/tex]Therefore, the answer for double number line is:
Cans : 0 16 32 48 64 80
Percent : 0% 20% 40% 60% 80% 100%
B.
Based on the information gathered from A, for every 16 cans Liz collects, she adds 20% toward her goal. She will have 32 cans if she reaches 40% of her goal. Liz must collect 80 cans to reach her goal.
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Answer: ∠ABD = 19°
Step-by-step explanation:
The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.
Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD
90 - 71 = 19
Therefore ∠ABD = 19°
Answer:
m∠ABD = 19°
Step-by-step explanation:
Hello!
Recall that all angles of a rectangle are 90° in measure.
Angle B is 90°, and is made up of angles ABD and DBC.
We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.
Find ABDABC = ABD + DBC90 = ABD + 7119 = ABDSo the measure of angle ABD is 19°.
Draw the image of the figure under thegiven transformation.8. reflection across the y-axis
Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)
.
The coodinates of A(3,0) and after reflection A'(-3,0)
The coordinates B(1,4) and after reflection B'(-1,0)
The coordinates C(5,3) and after reflection C'(-5,3)
Plot the image on the graph
i need the fourth term of one and three all I need is the answers so I can quiz my son.
The formula for the nth term is expressed as
an = (an - 1)^2 - 3
This is a recursive formula
This means that the second term, a2 is
a2 = (a2 - 1)^2 - 3
a2 = (a1)^2 - 3
a2 = 4^2 - 3 = 16 - 3 = 13
a3 = (a3 - 1)^2 - 3
a3 = (a2)^2 - 3
a3 = 13^2 - 3 = 169 - 3 = 166
a4 = (a4 - 1)^2 - 3
a4 = (a3)^2 - 3
a4 = 166^2 - 3 = 27556 - 3 = 27553
Thus,
a4 = 27553
the company has been
According to the given diagram, we have 4 shirts in total, where there's only one short-sleeve white shirt, so we just have to divide 1/4
[tex]P=\frac{1}{4}=0.25[/tex]Then, we multiply by 100 to express it in percentage
[tex]P=0.25\cdot100=25[/tex]Hence, the answer is 25%.1. In the figure, angle CAB is 47. What would prove that angle ACD is also 47?
A A reflection of ABC over AC, such that ABC maps to CDA.
B A rotation of ABC 180 clockwise around C, such that ABC maps to ADC.
C A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
D A translation of ABC to the top right, such that ABC maps to ADC.
The correct option C: A rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC.
What is termed as the rotation?Geometry can be used to determine the meaning of rotation in mathematics. As a result, it is described as the movement of something around a center or an axis. Any rotation is regarded as a specific space motion that freezes at at least one point. In reality, a earth rotates on its axis, which is also an instance of rotation. Because a clockwise rotation has a negative magnitude, a counterclockwise rotation does have a positive magnitude.For the given question;
In triangles ABC angle CAB is 47.
If the triangles ABC and ACD becomes congruent such that angle ACD corresponds to angles ABC.
Then, both angles will be equal.
For, this, a rotation of ABC 180 counterclockwise around A, such that ABC maps to ADC is to be done.
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Where are the minimum and maximum values for f(x)A. min: x =2¹ 2Reset Selectionmax:z = = 0, π, 2πOB. min:z = π max:x = 0, 2OC. min:z = 0, 2π max:x = πOD. min:z = ,,max:x = 0, 3, 4,2=- 3 cos z - 2 on the interval [0, 2π]?2P
Given:
The function f(x) = 3cos(x) - 2.
Required:
What are the minimum and maximum value of function?
Explanation:
To check maximum and minimum value of function.
First derivate the original function.
After putting first derivative equal to zero, critical points can be found.
Then, do second deritvative to check points of maxima and minima.
The critical points at which second derivative greater than zero. Point will be of minima.
The critical points at which second derivative less than zero. Point will be of maxima.
So,
[tex]\begin{gathered} f(x)=3cos(x)-2 \\ \text{ First derivative} \\ f^{\prime}(x)=-3sinx \\ \text{ Put }f^{\prime}(x)=0 \\ sinx=0 \\ x=0,\pi,2\pi \end{gathered}[/tex]Now, do second derivative test for maximum and minimum points
[tex]\begin{gathered} f^{\prime}^{\prime}(x)=-3cosx \\ \text{ At }x=0 \\ f^{\prime}^{\prime}(0)=-3\times1=-3<0 \\ \text{ At }x=\pi \\ f^{\prime}^{\prime}(\pi)=-3\times cos(\pi)=-3\times-1=3>0 \\ At\text{ }x=2\pi \\ f^{\prime}^{\prime}(2\pi)=-3\times1=-3<0 \\ \end{gathered}[/tex]Answer:
[tex]\text{ The points }0,2\pi\text{ are points of maxima and }\pi\text{ giving minima.}[/tex]
Find the missing length of the triangle. 22 cm 17.6 cm The missing length is centimeters.
6+[(-9)+(-1)] what does this equal
-4
Explanation:
6+[(-9)+(-1)]
Open the bracket:
6 + (-9) + (-1)
Note: Multiplication of opposite signs give a negative number.
6 - 9 - 1
= 6 - 10
= -4
Which describes a line passing through (3,3) that is perpendicular to the line described by y=3/5x+2 ?
Given:
Point (3,3)
The equation of the line,
[tex]y=\frac{3}{5}x+2[/tex]To find the equation of the line that passes through (3,3) and is perpendicular to the line:
The perpendicular slope is,
[tex]m=-\frac{5}{3}[/tex]Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{5}{3}(x-3) \\ y=-\frac{5}{3}x+5+3 \\ y=-\frac{5}{3}x+8 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-\frac{5}{3}x+8[/tex]Let us find the intercepts.
When x=0, we get y=8
So, the y-intercept is (0,8).
When y=0, we get
[tex]\begin{gathered} -\frac{5}{3}x+8=0 \\ \frac{5}{3}x=8 \\ x=\frac{24}{5} \\ x=4.8 \end{gathered}[/tex]So, the x-intercept is (4.8,0).
Hence, the correct option which satisfies the equation of the line is D (last option).
Downhill RacerA snowboardertravels 105 metersin 7 seconds.A skier travels for4 seconds andcovers 72 metersHow far will a skier travel in 2minutes? Explain how you figured it out.
To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).
A skier travels for 4 seconds and covers 72 meters.
Constant Rate (Speed):
[tex]\text{ }\frac{\text{ Distance Traveled}}{\text{ Time}}\text{ = }\frac{\text{ 72 meters}}{\text{ 4 seconds}}\text{ = }18\text{ meters/second}[/tex]Determining the distance covered in 2 minutes:
Step 1: Convert the time in minutes into seconds.
[tex]\text{ 2 (minutes) x }\frac{\text{ 60 seconds}}{\text{ 1 (minute)}}\text{ = 2 x 60 seconds = 120 seconds}[/tex]Step 2: Multiply the time by the constant rate (speed) of the skier.
[tex]\text{ Distance Traveled = 120 (seconds) x }18\text{ }\frac{\text{ meters}}{\text{ (second)}}[/tex][tex]\text{ = 120 x 18 meters}[/tex][tex]\text{ Distance Traveled = 2,160 meters}[/tex]Therefore, in 2 minutes, the skier travels 2,160 meters.
Quantum Logic recently expanded its operations at a cost of $450,000. Management expects that the value of the investment will grow at a rate of 8% per year compounded quarterly for the next 5 years. Find the future value of the investment
Given:
Quantum Logic recently expanded its operations at a cost of $450,000.
So, P = 450,000
The rate of growth = r = 8% = 0.08
compounded quarterly, n = 4
We will find the future value of the investment (A) after t = 5 years
We will use the following formula:
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]Substitute with the given values:
[tex]\begin{gathered} A=450,000\cdot(1+\frac{0.08}{4})^{4\cdot5} \\ \\ A=450,000\cdot1.02^{20}\approx668,676.33 \end{gathered}[/tex]So, the answer will be:
The future investment = $668,676.33
ok so this is multiplying decimals 7.3 x9.6=please show your work and answer thank you
therefore, the answer is 70.08
Explanation
Step 1
first multiply as if there is no decimal
[tex]\begin{gathered} 7.3\cdot9.6 \\ a)7.3\cdot9.6\Rightarrow73\cdot96 \\ 73\cdot69=7008 \end{gathered}[/tex]Step 2
count the number of digits after the decimal in each factor.
[tex]\begin{gathered} 7.3\Rightarrow1\text{ decimal} \\ 9.6\Rightarrow1\text{ decimal} \\ \text{total }\Rightarrow2\text{ decimals} \end{gathered}[/tex]
Step 3
Put the same number of digits behind the decimal in the product
[tex]7008\Rightarrow put\text{ 2 decimal, }\Rightarrow so\Rightarrow70.08[/tex]therefore, the answer is 70.08
I hope this helps you
Given m||n, find the value of x.50°Click heredismiss)
Let's recall that If a set of 2 parallel lines, line m and line m, are crossed or cut by another line, line T, in our question, we say "a set of parallel lines are cut by a transversal.
Each of the parallel lines cut by the transversal has 4 angles surrounding the intersection.
These are matched in measure and position with a counterpart at the other parallel line.
At each of the parallel lines, there are two pairs of vertical angle. Each angle in the pair is congruent to the other angle in the pair.
In our question, the angle that measures 145 degrees is congruent with the opposites angles of angle x.
Let's recall that x and 145 degrees are adjacent supplementary angles. And these angles add up to 180 degrees. Then, for solve for x, we have:
x = 180 - 145
x = 35 degrees